Electromagnetic field prediction method applied to linear propulsion electromagnetic energy equipment

Abstract

The invention provides an electromagnetic field prediction method applied to linear propulsion electromagnetic energy equipment, and the method comprises the steps: taking numerical simulation data as input, and taking electromagnetic parameters as constraint conditions to guide a model to generate electromagnetic field distribution at a corresponding moment, and the electromagnetic parameters at least comprise excitation current, armature conductivity and time; the method comprises the following steps: constructing a U-net structure which takes a short residual error and a convolution Transform as a Backbone, and taking the U-net structure as a core network of a conditional diffusion model, and establishing a CT-Unet-CDDPM model; and combining the data of the numerical simulation stable stage with the data of the deep learning calculation'pseudo oscillation 'stage to obtain the electromagnetic field of the linear propulsion electromagnetic energy equipment in the whole launching process at the high speed. According to the method, high-precision extrapolation calculation of the electromagnetic field at a high speed is realized, and a new thought is provided for analysis and optimization of emission performance of linear propulsion electromagnetic energy equipment.

Description

Technical Field

[0001] The present application belongs to the technical field of launch performance analysis of linear propulsion electromagnetic energy equipment, and in particular, relates to an electromagnetic field prediction method applied to linear propulsion electromagnetic energy equipment. Background Art

[0002] Linear propulsion electromagnetic energy equipment is a device that converts electromagnetic energy into kinetic energy. It has the advantages of high efficiency, fast start-up, and good reliability. It has broad application prospects in both military and civilian fields. The transient change of its current and the structural differences of different launch systems will lead to uneven distribution of the physical field in the guide rail and the armature. Excessive local current density will cause the armature to generate a lot of heat during high-speed launch, causing severe ablation or even vaporization of the armature-rail contact area. Therefore, analyzing the electromagnetic field distribution on the rail cross section and the armature-rail contact surface during the armature launch process is of great significance to improving the launch efficiency and service life of linear propulsion electromagnetic energy equipment.

[0003] In recent years, deep learning has driven tremendous changes in various fields with its powerful feature extraction, generalization, and nonlinear modeling capabilities. Deep learning methods are mainly based on CNN architectures, and are combined with a variety of advanced network architectures to achieve efficient and high-precision field prediction. For example, CNN and residual networks (ResNet) are used to extract complex nonlinear features in physical field data, and residual blocks are used to solve the gradient vanishing problem in deep networks, thereby improving the stability and prediction accuracy of the model; Transformer is used to process sequence data, and the dependency between physical fields and long-distance time t is captured through the self-attention mechanism to achieve accurate modeling; the generator and discriminator in the Generative Adversarial Networks (GAN) are trained against each other, the generator generates realistic physical field distributions, and the discriminator is continuously optimized to distinguish between real data and generated data, thereby improving the quality of the generated results. However, GAN has the problems of poor interpretability and difficulty in training. The VIT (Vision Transformer) proposed by DosoVITskiy et al., unlike the traditional CNN that extracts feature information through convolution, divides the image into patches, and uses a multi-head attention mechanism to calculate the relationship between patches and all features, which can better learn global information. The U-VIT model proposed in the literature uses VIT as the core architecture of the diffusion model, and its performance is better than or equivalent to that of the CNN-based U-Net in multiple tasks. However, VIT requires a large number of samples, computing resources, and memory. In addition, VIT divides images into patches for input into the model, resulting in loss of spatial information and lack of local perception mechanisms. It may perform poorly in the initial training stage and requires more training iterations, larger datasets, and complex training strategies to converge. Summary of the invention

[0004] In view of this, the present application aims to propose an electromagnetic field prediction method applied to linear propulsion electromagnetic energy equipment to solve at least one of the above problems.

[0005] To achieve the above purpose, the technical solution of this application is implemented as follows:

[0006] The present application provides an electromagnetic field prediction method applied to linear propulsion electromagnetic energy equipment, including:

[0007] The numerical simulation data is used as input, and the electromagnetic parameters are used as constraints to guide the model to generate the electromagnetic field distribution at the corresponding time, wherein the electromagnetic parameters at least include the excitation current, the armature conductivity, and the time;

[0008] Construct a U-net structure with short residual and convolutional Transformer as the backbone, and use it as the core network of the conditional diffusion model to establish the CT-Unet-CDDPM model;

[0009] The data from the stable phase of numerical simulation is combined with the data from the "pseudo-oscillation" phase calculated by deep learning to obtain the electromagnetic field of the high-speed linear propulsion electromagnetic energy equipment during the entire launch process.

[0010] Furthermore, the CT-Unet-CDDPM model is composed of an encoder, a decoder, a noise addition module and a conditional input. The backbone network of the conditional diffusion model is an end-to-end U-net model composed of an encoder and a decoder as a generator. The U-net model is used to extract features from noisy images, wherein each encoder and decoder is composed of a CT module, layer normalization, and a Swish activation function.

[0011] Further, numerical simulation data at different time points and under different conditions are collected, the numerical simulation data are interpolated and matrixed, and converted into a single-channel two-dimensional field map in the form of an image;

[0012] Performing maximum-minimum normalization and standardization processing on the single-channel two-dimensional field map to construct a data set for model training, and randomly dividing the data set into a training set and a test set;

[0013] The predicted output is the denoised image.

[0014] Furthermore, the CT-Unet-CDDPM model training process includes:

[0015] In the training phase, the electromagnetic parameters are concatenated and combined to form a conditional vector to establish a one-to-one mapping from the electromagnetic parameters to the corresponding electromagnetic field, including:

[0016] The normalized conditional vectors are spliced ​​in a fixed order, and the spliced ​​conditional vectors are input into the middle layer between the encoder and the decoder, where the excitation current, armature conductivity, and time t correspond to vectors i, σ, and t, respectively, to form a conditional vector;

[0017] The conditional vector is concatenated with the features extracted by the encoder in the middle layer and combined with the current field I under the corresponding condition. iσt , magnetic flux density field B iσt Composition {(i,σ,t),I iσt / Biσt} data pairs to form a joint conditional vector, so that the features received by the decoder contain conditional information. In each denoising process of the decoder, the input of the model includes the current noise data, time step, and joint conditional vector. The specific formula is expressed as:

[0018] x t-1 =x t -ε θ (x t ,t,c);

[0019] In the formula, ε θ represents a parameterized denoising function that depends on the current noise data, time step, and joint condition vector;

[0020] In the testing phase, the noise data, time step and joint condition vector with the same dimensions as the input data are input into the trained model to generate the electromagnetic field distribution map at the corresponding moment.

[0021] Furthermore, the model is automatically tuned through the Optuna hyperparameter optimization framework, including:

[0022] The model optimizer uses an adaptive momentum estimation optimizer and a cosine annealing algorithm to dynamically adjust the learning rate. The formula is as follows:

[0023]

[0024] In the formula, Represents the range of learning rate, T cur Represents the current iteration number, T i Represents the number of iterations in a cycle.

[0025] Furthermore, in the process of comparative analysis of the field prediction experiment, the mean square error and mean absolute percentage error are used as the performance indicators of the CT-Unet-CDDPM model to evaluate the accuracy of the predicted electromagnetic field distribution, and the formula is:

[0026]

[0027] In the formula, yi and are the true value and predicted value of the i-th sample respectively, and N is the number of samples.

[0028] Furthermore, the electromagnetic field control equation of the linear propulsion electromagnetic energy equipment is a convection-diffusion type. The Peclet number is used as the leading role of the convection term in the evaluation equation. The Peclet number formula is:

[0029]

[0030] In the formula, h c is the unit grid size, σ is the conductivity, v is the armature motion speed, and μ is the relative magnetic permeability.

[0031] Compared with the prior art, the electromagnetic field prediction method for linear propulsion electromagnetic energy equipment described in this application has the following beneficial effects:

[0032] The electromagnetic field prediction method applied to linear propulsion electromagnetic energy equipment described in this application realizes high-precision extrapolation calculation of the electromagnetic field at high speed, providing a new idea for the launch performance analysis and optimization of linear propulsion electromagnetic energy equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0034] Figure 1 This is a flow chart of an electromagnetic field prediction method applied to linear propulsion electromagnetic energy equipment described in an embodiment of the present application;

[0035] Figure 2 This is a schematic diagram of the CT module structure described in the embodiment of the present application;

[0036] Figure 3 This is a schematic diagram of the CT-Unet structure described in the embodiment of the present application;

[0037] Figure 4 This is a schematic diagram of the diffusion model described in the embodiment of the present application;

[0038] Figure 5 This is a schematic diagram of the CT-Unet-CDDPM model described in the embodiment of the present application. DETAILED DESCRIPTION

[0039] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below in combination with specific embodiments and with reference to the accompanying drawings.

[0040] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the embodiments of the present application should be the usual meanings understood by people with ordinary skills in the field to which the present application belongs. The "first", "second" and similar words used in the embodiments of the present application do not represent any order, quantity or importance, but are only used to distinguish different components. "Including" or "comprising" and similar words mean that the elements or objects appearing in front of the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0041] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0042] See also Figure 1 As shown, this embodiment provides an electromagnetic field prediction method applied to linear propulsion electromagnetic energy equipment, which specifically includes the following steps:

[0043] Step S101 : taking numerical simulation data as input, and taking electromagnetic parameters as constraints to guide the model to generate electromagnetic field distribution at a corresponding time, wherein the electromagnetic parameters at least include excitation current, armature conductivity, and time.

[0044] Step S102: construct a U-net structure with short residual and convolutional Transformer as the backbone, and use it as the core network of the conditional diffusion model to establish a CT-Unet-CDDPM model.

[0045] Step S103: Combine the data of the stable phase of the numerical simulation with the data of the "pseudo-oscillation" phase of the deep learning calculation to obtain the electromagnetic field of the high-speed linear propulsion electromagnetic energy equipment during the entire launching process.

[0046] Specifically, in this embodiment, due to the drastic change of the electromagnetic field during the launch of the linear propulsion electromagnetic energy equipment, this embodiment uses convolution operation to replace the block operation of VIT, establishes a CT module, and uses it as the core network of U-Net in the diffusion model to improve the high-resolution generation capability of the electromagnetic field and reduce the sample requirements. Finally, the convolution, Transformer and diffusion models are combined to establish the CT-Unet-CDDPM model. The excitation current, armature conductivity, time t, etc. are used as constraints to guide the CT-Unet-CDDPM model to directly generate the electromagnetic field under the corresponding parameters, especially the high-precision extrapolation calculation of the electromagnetic field in the "pseudo-oscillation" stage. For the problem of insufficient training data, the armature conductivity is reduced to varying degrees, the stable simulation time is extended, and the training data set is increased. Furthermore, the model can learn the changing law of the electromagnetic field under different conductivity conditions and improve the generalization ability of the extrapolation calculation under the reference conductivity. At the same time, the Optuna hyperparameter optimization framework is used to realize the automatic parameter adjustment of the model. Finally, the electromagnetic field of the linear propulsion electromagnetic energy equipment at high speed is quickly and accurately calculated during the entire launch process.

[0047] The electromagnetic field prediction method described in this embodiment has an average absolute percentage error of approximately 1.9% and 2.6% for the interpolation of low-speed calculation examples and the extrapolation of high-speed calculation examples, respectively, which can meet engineering requirements. The research results have achieved high-precision extrapolation calculation of electromagnetic fields at high speeds, providing new ideas for the analysis and optimization of the launch performance of linear propulsion electromagnetic energy equipment.

[0048] In this embodiment, the conditional diffusion model used is the denoising diffusion probabilistic model (DDPM), whose principle comes from the molecular diffusion motion in non-equilibrium thermodynamics. Two Markov chains are defined to add noise and remove noise from the data, which consists of a forward denoising diffusion process and a trainable reverse diffusion denoising process.

[0049] Since the original diffusion model does not incorporate conditional information into the generation process, the generated content is uncontrollable. The conditional diffusion model guides the generation of images through specified constraints, reducing sample diversity and increasing the relevance of generated data.

[0050] This embodiment adopts Classifier-Free Guidance because it does not require additional classifier training, reduces dependence on external components, and provides better training stability and generation quality, especially in high-resolution and complex scenes.

[0051] Since the introduction of condition y has no effect on the previous diffusion process, after adding additional information, the joint probability of the reverse process of the conditional diffusion model is:

[0052]

[0053] Combined with the given condition y, the Gaussian distribution that the model needs to learn becomes p θ (x0|x t ,y), then the objective function is defined as:

[0054]

[0055] At this time, the sampling step length of the conditional diffusion model is

[0056]

[0057] In this embodiment, only the electromagnetic field value is used as the input x0, and the excitation current, armature conductivity, and time t are input into the diffusion model as the condition y, so as to realize a one-to-one mapping between the data in the recommended data set and the corresponding physical field diagram generated during the sampling process.

[0058] In this embodiment, for the CT-Unet model, in order to solve the problems of lack of local bias and insufficient early feature extraction capability in VIT, this embodiment improves the VIT module and proposes a CT module. The structure diagram is as follows: Figure 2 As shown in the figure, the CT module is used as the backbone of the U-net model to build the CT-Unet model, and residual links are added before and after each CT module to prevent network degradation. The structure is as follows Figure 3 shown.

[0059] This embodiment replaces the block operation in VIT with a convolution layer, which controls the token feature dimension and the number of tokens at each stage by adjusting the parameters of the convolution operation. The input data is converted into Patches of fixed size through the convolution operation, and each patch is flattened into a one-dimensional vector. Then, these vectors are mapped to a fixed-dimensional feature space through linear projection, and position encoding is added to retain spatial information. Finally, these processed patch feature vector sequences are used as the input of the multi-head attention mechanism.

[0060] The CT module makes full use of the local feature extraction capability of the convolution operation and the global feature capture capability of the Transformer multi-head attention mechanism, overcoming the problems of VIT requiring a long training time and insufficient generalization ability under small sample data sets, thereby realizing the combination of CNN and Transformer, allowing CVT to accept inputs of any size, with a stronger ability to perceive local features while reducing computational costs.

[0061] In addition, the electromagnetic field of the linear propulsion electromagnetic energy equipment changes dramatically under high-speed operation, and the field intensity gradient on the contact surface between the track section and the pivot rail changes greatly. The CT module first extracts the features of the local electromagnetic field value, aiming to learn the variation law of the field intensity gradient in some areas. The Patches with gradient change information extracted by convolution are input into the Transformer module, and the field intensity gradient information of some areas is further linked to the global features, thereby improving the model's ability to generate complex electromagnetic fields. This embodiment uses the U-net model including the CT module and residual links as the core network of the diffusion model.

[0062] In this embodiment, the CT-Unet-CDDPM model used is mainly composed of an encoder, a decoder, a noise adding module and a conditional input. Figure 4 As shown in Figure 2, the backbone network of the diffusion model uses an end-to-end U-net model consisting of an encoder and a decoder as a generator, where the U-net model extracts features from the noisy image and uses these features to reconstruct a clear image.

[0063] Specifically, numerical simulation data at different time points and under different conditions are collected, and then these data are interpolated and matrixed to convert the electromagnetic field data into a single-channel two-dimensional field map in the form of an image, with a resolution of 256×64 on the track section and 256×256 on the contact surface of the pivot rail. These data are normalized and standardized to normalize the data range to [-1,1] to improve model performance and training efficiency. Finally, the processed data set is randomly shuffled and divided into a training set and a test set in a ratio of 8:2 as the data set input into the model.

[0064] The forward process is to gradually add noise of different intensities to the data set through a predefined scheme until the data is converted into pure noise. The reverse process relies on the encoder-decoder to extract the features of the noise data layer by layer through the encoder, refine and restore the details of the image layer by layer in the decoder, and finally the output of the model is the prediction of the denoised image.

[0065] Each encoder and decoder in the CT-Unet-CDDPM model consists of a CT module, layer normalization (LN), and a Swish activation function. The LN layer is used instead of a batch normalization layer to maintain consistency with the CT module and to improve the model's stability and adaptability to images of different sizes and small batches of data. The introduction of the monotonic and smooth Swish activation function can provide a more stable gradient and improve the stability and convergence speed during training.

[0066] During the training phase, it is necessary to establish a one-to-one mapping from multiple conditions such as excitation current, armature conductivity, time t, etc. to the corresponding electromagnetic field. Therefore, the conditional constraints need to be spliced ​​and combined into a conditional vector. Specifically, the normalized conditional vectors are spliced ​​in a fixed order to form a long vector. The excitation current, armature conductivity, and time t correspond to vectors i, σ, and t, respectively, to form a joint conditional vector. The input in the middle layer between the encoder and the decoder helps to retain the conditional information in the process of restoring the extracted complex features to the original data distribution. The joint conditional vector is spliced ​​with the features extracted by the encoder in the middle layer, and the current field Iiσt and the magnetic flux density field Biσt under the corresponding conditions are combined to form a data pair of {(i, σ, t), Iiσt / Biσt} to ensure that the features received by the decoder contain conditional information. In each denoising process of the decoder, the input of the model includes the current noise data, time step, and joint conditional vector. The model not only denoises based on the current noise data, but also needs to consider the conditional constraints. The specific implementation method is

[0067] x t-1 =x t -ε θ (x t ,t,c)

[0068] In the formula, ε θ It is a parameterized denoising function that depends on the current noise data, time step and condition vector. The loss is calculated by comparing the generated image with the original data to update the parameters of the neural network.

[0069] In the test phase, Gaussian random noise of the same dimension as the input data, time t and other conditions are input into the trained model, and the electromagnetic field distribution map at the corresponding time can be directly generated from the Gaussian noise, such as Figure 5 shown.

[0070] In this embodiment, the numerical simulation process of the linear propulsion electromagnetic energy equipment is a complex electromagnetic thermal multi-field coupling solution process. This embodiment uses COMSOL finite element software to establish a finite element simulation model that considers electromagnetic thermal multi-physics field coupling to calculate and solve the linear propulsion electromagnetic energy equipment. In the numerical simulation process, the following basic assumptions are made:

[0071] (1) The armature and the track are in good contact, ignoring the unevenness of the contact interface and the wear of the material.

[0072] (2) During the launch process, the generation of molten aluminum at the interface of the pivot rail will cause the sliding friction coefficient to decrease sharply and tend to be stable. In order to simplify the calculation, it is assumed that the sliding friction coefficient remains constant at 0.11 throughout the launch process.

[0073] (3) To improve the convergence of the model calculation, the outer side of the track is set as a rigid material.

[0074] According to the multi-physics control equation, the model parameters of the pivot rail and the excitation current, a finite element simulation model under ideal contact conditions is established, and the values ​​of the parameters of the armature dynamic equation are shown in Table 1. Considering the influence of skin effect and proximity effect on current distribution, the mesh on the inner side of the track is divided more finely. At the same time, due to the drastic changes in the physical field at the pivot rail contact surface, the mesh in this area is also processed more carefully. During the transient solution process, the time step is set to 0.001ms and the calculation tolerance is set to 0.01.

[0075] Table 1 Parameters of armature dynamic equation

[0076] parameter Numeric <![CDATA[Coefficient of friction μ f > 0.11 <![CDATA[Mechanical preloading pressure F N,p / N]]> 6 770 Air specific heat ratio γ 1.40 <![CDATA[Initial air density ρ0 / (kg·m -3 )]]> 1.29 <![CDATA[Armature cross-sectional area S / m 2 > <![CDATA[6.25×10 -4 ]]> Armature cross-section circumference L / m 0.10 <![CDATA[Coefficient of viscous friction C f > <![CDATA[3.00×10 -3 ]]>

[0077] Both cases take the C-shaped armature linear propulsion electromagnetic energy equipment as the research object, and use COMSOL software for finite element modeling. The setting of model size, parameters and structure is the key to the study of electromagnetic field characteristics of linear propulsion electromagnetic energy equipment. Armature structures of different shapes have different armature-rail contact states, launch efficiency and reliability performance, but their response trends to objective laws during the launch process are consistent. The current generated by the power module flows in from the lower end face of track A, passes through the armature and flows out from the lower end face of track B, forming a closed loop.

[0078] As the structure of deep learning models becomes increasingly complex, the number of hyperparameters involved increases, making manual adjustment of model hyperparameters difficult and inefficient. Automated parameter adjustment can find a better hyperparameter configuration, optimize through a systematic optimization algorithm, reduce reliance on manual experience, and save a lot of time and computing resources. TPE (Tree-structured parzen estimator, TPE) is a hyperparameter optimization algorithm based on the Bayesian optimization framework. It simulates the distribution of hyperparameters by constructing two different probability density functions (Probability density functions, PDFs) for better and worse results of the objective function. TPE's strategy for selecting the next set of hyperparameters is based on the ratio of these two PDFs, giving priority to hyperparameters that can improve the objective function. Compared with the traditional Gaussian process method, TPE shows higher efficiency and flexibility in dealing with large-scale parameter spaces and multi-parameter scenarios.

[0079] The model optimizer uses the adaptive momentum estimation optimizer (Adam), which combines the advantages of the AdaGrad algorithm and the RMSPro algorithm. Compared with the traditional stochastic gradient descent (SGD) algorithm, Adam is less likely to fall into the local optimum and has a fast update speed. On this basis, the cosine annealing algorithm is used to dynamically adjust the learning rate, gradually reducing the learning rate from the initial value to a smaller value. In each cycle, the learning rate first decreases and then increases, providing an effective method to find the global optimal solution and optimize the model performance. The formula is

[0080]

[0081] In the formula, Represents the range of learning rate, T cur Represents the current iteration number, T i Represents the number of iterations in a cycle, that is, after reaching this number of iterations, the learning rate will be reset to the maximum value.

[0082] Evaluation indicators

[0083] In the process of comparative analysis of field prediction experiments, mean square error (MSE) and mean absolute percentage error (MAPE) are used as performance indicators of the CT-Unet-CDDPM model to evaluate the accuracy of predicting electromagnetic field distribution. The formula is:

[0084]

[0085] In the formula, y i and are the true value and predicted value of the i-th sample respectively, and N is the number of samples.

[0086] Extrapolation prediction method of electromagnetic field at high speed

[0087] The electromagnetic field control equation of the linear propulsion electromagnetic energy equipment is a convection-diffusion type, and the influence of speed is mainly reflected in the convection term of the equation. The Peclet number, as a dimensionless parameter, is mainly used to evaluate the dominant role of the convection term in the equation, and it reflects the stability of the numerical solution of the equation. The formula for calculating the Peclet number is

[0088]

[0089] In the formula, h c is the unit grid size, σ is the conductivity, v is the armature motion speed, and μ is the relative magnetic permeability.

[0090] From the formula, we can see that P eThe number is proportional to the mesh cell size, velocity, conductivity, and magnetic permeability. As velocity increases, P e Gradually increases. e >1, the characteristic of "pivot dominance" of the matrix of the discrete equation system will be weakened, resulting in the matrix becoming ill-conditioned and the numerical solution showing "pseudo-oscillation" that does not exist physically. In order to avoid the "pseudo-oscillation" phenomenon, a very fine grid must be used. However, under the conditions of high speed, high magnetic permeability and high electrical conductivity, it is difficult to make P e The grid division with a value of <1 requires too much computation and consumes too much computer resources, so it is not advisable in practice.

[0091] In order to obtain the electromagnetic field of the entire launching process of the linear propulsion electromagnetic energy equipment at high speed, this embodiment uses a deep neural network to extract the electromagnetic field distribution characteristics and learn the distribution law of the field, thereby extrapolating the electromagnetic field distribution at high speed to the "pseudo-oscillation" stage.

[0092] In order to achieve efficient training, deep learning networks usually require a large amount of data. However, the stable numerical simulation time of high-speed linear propulsion electromagnetic energy equipment only under standard conductivity conditions is too short, resulting in insufficient training data under actual conductivity that can be used for training, which in turn affects the prediction accuracy of the trained model in the extrapolation task. To this end, this embodiment adopts a strategy of numerical simulation under 100%, 80%, 60% and 40% armature conductivity conditions, and prolongs the time length of stable simulation by reducing the armature conductivity, thereby increasing the amount of data available for training.

[0093] By training on electromagnetic field data under different conductivities, the model can learn the changing laws of the electromagnetic field under different conductivities, thereby improving the generalization ability in the extrapolation task under the baseline conductivity. It should be emphasized that although numerical simulation by reducing the armature conductivity is meaningless in actual engineering applications, the prediction of the model under different conductivities can be regarded as solving multiple problems with similar control equations. This enables the deep neural network to learn the laws of electromagnetic field distribution, thereby improving the prediction accuracy under standard conductivity conditions.

[0094] Therefore, this embodiment uses numerical simulation data under different conductivities to train CT-Unet-CDDPM to solve the "pseudo-oscillation" problem in high-speed conditions, and predicts the electromagnetic field distribution in the "pseudo-oscillation" stage under reference conductivity by extrapolation.

[0095] Embodiment, the electromagnetic field prediction method under high speed based on CT-Unet-CDDPM is as follows:

[0096] 1) Data sampling. By establishing a three-dimensional finite element simulation model of the linear propulsion electromagnetic energy equipment, the distribution of different electromagnetic fields on the track cross section and the contact surface of the pivot rail during the launch process is calculated. Based on the stability of the numerical solution, the obtained numerical solution is divided into a stable stage and a "pseudo-oscillation" stage.

[0097] 2) Data preprocessing: Perform maximum and minimum normalization and standardization on the data and divide it into training sets and test sets to help the model learn and identify patterns in the data more effectively and improve the accuracy and efficiency of the model.

[0098] 3) Build and train a deep learning model. Build the CT-Unet-CDDPM model and train the model using the training set. Test the prediction accuracy of the model on the test set to evaluate whether the model has learned the potential electromagnetic field distribution law in the data.

[0099] 4) Extrapolation prediction. Using the trained CT-Unet-CDDPM model, the predicted electromagnetic field distribution in the stable phase of the numerical solution is compared with the results obtained by numerical simulation calculations to verify the accuracy of the model. Then, the trained model is used to predict the electromagnetic field distribution in the "pseudo-oscillation" phase at high speed at the base conductivity. The numerical simulation results in the stable phase of the numerical solution and the predicted results in the "pseudo-oscillation" phase are combined to obtain the electromagnetic field of the entire launch process.

[0100] The results show that compared with basic and advanced models such as U-net, CGAN, Unet-CGAN, CT-Unet, and Unet-DDPM, the CT-Unet-CDDPM model has the highest accuracy. For the example verification of the interpolation calculation of the US low-speed linear propulsion electromagnetic energy equipment and the extrapolation calculation of the South Korean high-speed linear propulsion electromagnetic energy equipment, the MAPE on the test set was approximately 1.9% and 2.6%, respectively, which can generate more refined electromagnetic fields.

[0101] It should be noted that the above describes some embodiments of the present application. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the above embodiments and still achieve the desired results. In addition, the processes depicted in the accompanying drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0102] The embodiments of the present application are intended to cover all such substitutions, modifications and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the embodiments of the present application should be included in the scope of protection of the present application.

Claims

1. An electromagnetic field prediction method applied to linear propulsion electromagnetic energy equipment, characterized in that: include: The numerical simulation data is used as input, and the electromagnetic parameters are used as constraints to guide the model to generate the electromagnetic field distribution at the corresponding time, wherein the electromagnetic parameters at least include the excitation current, the armature conductivity, and the time; Construct a U-net structure with short residual and convolutional Transformer as the backbone, and use it as the core network of the conditional diffusion model to establish the CT-Unet-CDDPM model; The data from the stable phase of numerical simulation is combined with the data from the "pseudo-oscillation" phase calculated by deep learning to obtain the electromagnetic field of the high-speed linear propulsion electromagnetic energy equipment during the entire launch process.

2. The method according to claim 1, characterized in that: The CT-Unet-CDDPM model consists of an encoder, a decoder, a noise addition module and a conditional input. The backbone network of the conditional diffusion model is an end-to-end U-net model consisting of an encoder and a decoder as a generator. The U-net model is used to extract features from noisy images, wherein each encoder and decoder consists of a CT module, layer normalization, and a Swish activation function.

3. The method according to claim 2, characterized in that: Collecting numerical simulation data at different time points and under different conditions, interpolating and matrixing the numerical simulation data, and converting the data into a single-channel two-dimensional field map in the form of an image; Performing maximum-minimum normalization and standardization processing on the single-channel two-dimensional field map to construct a data set for model training, and randomly dividing the data set into a training set and a test set; The predicted output is the denoised image.

4. The method according to claim 3, characterized in that: The CT-Unet-CDDPM model training process includes: In the training phase, the electromagnetic parameters are concatenated and combined to form a conditional vector to establish a one-to-one mapping from the electromagnetic parameters to the corresponding electromagnetic field, including: The normalized conditional vectors are spliced ​​in a fixed order, and the spliced ​​conditional vectors are input into the middle layer between the encoder and the decoder, where the excitation current, armature conductivity, and time t correspond to vectors i, σ, and t, respectively, to form a conditional vector; The conditional vector is concatenated with the features extracted by the encoder in the middle layer and combined with the current field I under the corresponding condition. iσt , magnetic flux density field B iσt Composition {(i,σ,t),I iσt / Biσt } data pairs to form a joint conditional vector, so that the features received by the decoder contain conditional information. In each denoising process of the decoder, the input of the model includes the current noise data, time step, and joint conditional vector. The specific formula is expressed as: x t-1 =x t -ε θ (x t ,t,c); In the formula, ε θ represents a parameterized denoising function that depends on the current noise data, time step, and joint condition vector; In the testing phase, the noise data, time step and joint condition vector with the same dimensions as the input data are input into the trained model to generate the electromagnetic field distribution map at the corresponding moment.

5. The method according to claim 2, characterized in that: The Optuna hyperparameter optimization framework is used to automatically adjust the model parameters, including: The model optimizer uses an adaptive momentum estimation optimizer and a cosine annealing algorithm to dynamically adjust the learning rate. The formula is as follows: In the formula, Represents the range of learning rate, T cur Represents the current iteration number, T i Represents the number of iterations in a cycle.

6. The method according to claim 1, characterized in that: In the process of comparative analysis of field prediction experiments, mean square error and mean absolute percentage error are used as performance indicators of the CT-Unet-CDDPM model to evaluate the accuracy of predicting electromagnetic field distribution. The formula is: In the formula, y i and are the true value and predicted value of the i-th sample respectively, and N is the number of samples.

7. The method according to claim 1, characterized in that The electromagnetic field control equation of the linear propulsion electromagnetic energy equipment is a convection-diffusion type. The Peclet number is used as the leading role of the convection term in the evaluation equation. The Peclet number formula is: In the formula, h c is the unit grid size, σ is the conductivity, v is the armature motion speed, and μ is the relative magnetic permeability.

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